二维格子气自动机模拟孔隙介质的电传输特性

本文应用2-D格子气自动机模拟饱和油水两相的多孔介质的导电特性。在油水两相界面处,引入反射与透射系数来决定粒子的运动状态,通过调节反射与透射系数就可以改变油水两相的导电性差异。用模拟结果考察Archie公式的地层因素F=R0/Rw和电阻率增大系数I=Rt/R0,其中,R0为百分之百饱和水时的岩石电阻率,Rw为水的电阻率,Rt为不同流体饮和度时的岩石电阻率。结果表明F与孔隙度φ间,I与含水饱和度间都存在幂关系,并可以表示为F=aφ-m,I=bS-nw模拟结果同时证实：公式中的参数a、m的变化反映了孔隙微观结构的变化,参数b、n主要受孔隙度大小和油相分布状态的影响。     

An improved gray lattice Boltzmann model for simulating fluid flow in multi-scale porous media

A lattice Boltzmann (LB) model is proposed for simulating fluid flow in porous media by allowing the aggregates of finer-scale pores and solids to be treated as ‘equivalent media’. This model employs a partially bouncing-back scheme to mimic the resistance of each aggregate, represented as a gray node in the model, to the fluid flow. Like several other lattice Boltzmann models that take the same approach, which are collectively referred to as gray lattice Boltzmann (GLB) models in this paper, it introduces an extra model parameter, n_s, which represents a volume fraction of fluid particles to be bounced back by the solid phase rather than the volume fraction of the solid phase at each gray node. The proposed model is shown to conserve the mass even for heterogeneous media, while this model and that model of Walsh et al. (2009) [1], referred to the WBS model thereafter, are shown analytically to recover Darcy–Brinkman’s equations for homogenous and isotropic porous media where the effective viscosity and the permeability are related to n_s and the relaxation parameter of LB model. The key differences between these two models along with others are analyzed while their implications are highlighted. An attempt is made to rectify the misconception about the model parameter n_s being the volume fraction of the solid phase. Both models are then numerically verified against the analytical solutions for a set of homogenous porous models and compared each other for another two sets of heterogeneous porous models of practical importance. It is shown that the proposed model allows true no-slip boundary conditions to be incorporated with a significant effect on reducing errors that would otherwise heavily skew flow fields near solid walls. The proposed model is shown to be numerically more stable than the WBS model at solid walls and interfaces between two porous media. The causes to the instability in the latter case are examined. The link between these two GLB models and a generalized Navier–Stokes model [2] for heterogeneous but isotropic porous media are explored qualitatively. A procedure for estimating model parameter n_s is proposed.     

Wavefield simulation in porous media saturated with two immiscible fluids

Wavefields in porous media saturated by two immiscible fluids are simulated in this paper. Based on the sealed system theory, the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation (capillary pressure). So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory. The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported. In our work, wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived. Furthermore, the wavefield and its characteristics are studied using the numerical finite element method. The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band. The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase. More specifically, the displacement decreases with increasing relaxation coefficient.     

Homogenization of saturated double porous media with Eshelby-like velocity field

In this paper, we focus on strength properties of double porous materials having a Drucker-Prager solid phase at microscale. The porosity consists in two populations of micropores and mesopores saturated with different pressures. To this end, we consider a hollow sphere subjected to a uniform strain rate boundary conditions. For the microscale to mesoscale transition, we take advantage of available results by Maghous et al. (2009), while the meso to macro upscaling is performed by implementing a kinematical limit analysis approach using Eshelby-like trial velocity fields. This two-step homogenization procedure delivers analytical expression of the macroscopic criterion for the considered class of saturated double porous media. This generalizes and improves previous results established by Shen et al. (2014). The results are discussed in terms of the existence or not of effective stresses. Some illustrations are provided.     

Pseudo Rayleigh wave in a partially saturated non-dissipative porous solid

Propagation of surface waves is studied at the pervious boundary of a porous solid saturated with a mixture of two immiscible fluids. An approach, based on continuum mixture theory, is used to derive a secular equation for the propagation of harmonic waves at the stress-free plane surface of this non-dissipative medium. Numerical analysis shows that this secular equation may not represent the propagation of true surface wave in the porous aggregate. Then, this equation is solved numerically for the propagation of pseudo Rayleigh wave or the leaky surface waves. To ensure the existence of pseudo Rayleigh wave, capillary effect between two (wetting and non-wetting) pore-fluids is related to the partial saturation. Effects of porosity and partial saturation coupled with capillary effect are observed on the phase velocity of pseudo Rayleigh waves in sandstone saturated with water-CO₂ mixture.     

Numerical analysis of bacterial transport in saturated porous media

A mathematical model to describe bacterial transport in saturated porous media is presented. Reversible/irreversible attachment and growth/decay terms were incorporated into the transport model. Additionally, the changes of porosity and permeability due to bacterial deposition and/or growth were accounted for in the model. The predictive model was used to fit the column experimental data from the literature, and the fitting result showed a good match with the data. Based on the parameter values determined from the literature experimental data, numerical experiments were performed to examine bacterial sorption and/or growth during bacterial transport through saturated porous media. In addition, sensitivity analysis was performed to investigate the impact of key model parameters for bacterial transport on the permeability and porosity of porous media. The model results show that the permeability and porosity of porous media could be altered due to bacterial deposition and growth on the solid matrix. However, variation of permeability due to bacterial growth was trivial compared with natural permeability variation. Copyright © 2005 John Wiley & Sons, Ltd.     

Effective parameters for flow in saturated heterogeneous porous media

Effective parameters for flow in saturated porous media are obtained via Taylor-Aris-Brenner moment analysis considering both periodic as well as stationary porous medium properties. It is assumed that a slug is instantaneously introduced into an unbounded, anisotropic porous medium having a compressible matrix, and that the correlation length of the local hydraulic conductivity and specific storage fluctuations is smaller than the correlation length of hydraulic head fluctuations (gradually varying flow). It is shown that the effective specific storage is equal to its volume average. The effective hydraulic conductivity is derived by a small-perturbation analysis and it is shown to consist of its volume average and of a second term which accounts for the ‘small’ local conductivity fluctuations.     

The stability of density-driven flows in saturated heterogeneous porous media

This work concludes the investigations into the stability of haline flows in saturated porous media. In the first part [33] a stability criterion for density-driven flow in a saturated homogeneous medium was derived excluding dispersion. In the second part [34], the effects of dispersion were included. The latter criterion made reasonable predictions of the stability regimes (indicated by the number of fingers present) as a function of density and dispersivity variations. We found out that destabilising variables caused an increase in the number of fingers and vice versa. The investigation is extended here for the effects of the medium heterogeneity. The cell problem derived via homogenization theory [20] is solved and its solution used to evaluate the elements of the macrodispersion tensor as functions of time for flow aligned parallel to gravity. The longitudinal coefficient exhibits asymptotic behaviour for favourable and moderately unfavourable density contrasts while it grows indefinitely for higher density contrasts. The range of densities stabilised by medium heterogeneities can thus be estimated from the behaviour of the coefficient. The d³f software program is used for the numerical simulations. The code uses the cell-centred finite volume and the implicit Euler techniques for the spatial and temporal discretisations respectively.     

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap,combined with variable grid-size and time-step,this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.     

A viscous boundary for transient analyses of saturated porous media

An absorbing boundary for saturated porous media is developed that can be used for transient analyses in the time domain. The elastic constitutive equations for the saturated porous media follow Bowen's formulation. The method consists of applying viscous tractions along the artificial boundary. The absorbing boundary behaviour is assumed linear and isotropic. Hadamard's conditions provide the speeds of the dilatational and shear waves that propagate in saturated porous media. Since these expressions are frequency independent, the intensities of the viscous tractions are evaluated in the time domain, and the two dilatational waves are accounted for. The viscous tractions are defined from the drained characteristics, assuming an infinite permeability, at variance with the traditional ‘undrained’ method based on undrained characteristics and a null permeability. Solid media and materials with low permeability are also retrieved as subcases. The results show that, at no additional cost, this ‘drained’ method is more accurate for all permeabilities than the ‘undrained’ method, which disregards the existence of the second dilatational wave. Copyright © 2003 John Wiley & Sons, Ltd.     

Directional interpolation infinite element for dynamic problems in saturated porous media

In this study, a directional interpolation infinite element suited to a saturated porous medium is presented to account for dynamic problems with semi-infi     

Analytical solutions for solute transport in saturated porous media with semi-infinite or finite thickness

Three-dimensional analytical solutions for solute transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, first-order decay of aqueous phase and sorbed solutes with different decay rates, and nonequilibrium solute sorption onto the solid matrix of the porous formation. The governing solute transport equations are solved analytically by employing Laplace, Fourier and finite Fourier cosine transform techniques. Porous media with either semi-infinite or finite thickness are considered. Furthermore, continuous as well as periodic source loadings from either a point or an elliptic source geometry are examined. The effect of aquifer boundary conditions as well as the source geometry on solute transport in subsurface porous formations is investigated.     

Role of chemotaxis in the transport of bacteria through saturated porous media

Populations of chemotactic bacteria are able to sense and respond to chemical gradients in their surroundings and direct their migration toward increasing concentrations of chemicals that they perceive to be beneficial to their survival. It has been suggested that this phenomenon may facilitate bioremediation processes by bringing bacteria into closer proximity to the chemical contaminants that they degrade. To determine the significance of chemotaxis in these processes it is necessary to quantify the magnitude of the response and compare it to other groundwater processes that affect the fate and transport of bacteria. We present a systematic approach toward quantifying the chemotactic response of bacteria in laboratory scale experiments by starting with simple, well-defined systems and gradually increasing their complexity. Swimming properties of individual cells were assessed from trajectories recorded by a tracking microscope. These properties were used to calculate motility and chemotaxis coefficients of bacterial populations in bulk aqueous media which were compared to experimental results of diffusion studies. Then effective values of motility and chemotaxis coefficients in single pores, pore networks and packed columns were analyzed. These were used to estimate the magnitude of the chemotactic response in porous media and to compare with dispersion coefficients reported in the field. This represents a compilation of many studies over a number of years. While there are certainly limitations with this approach for ultimately quantifying motility and chemotaxis in granular aquifer media, it does provide insight into what order of magnitude responses are possible and which characteristics of the bacteria and media are expected to be important.     

OpenGeoSys-Gem: A numerical tool for calculating geochemical and porosity changes in saturated and partially saturated media

Reactive transport codes that use a Gibbs Energy Minimization (GEM) to solve chemical equilibria are uncommon. We present a new coupling of the Richards flow module of the Finite Element (FE) based OpenGeoSys code with the GEM based chemical solver GEMS3K. The coupled code is highly parallelized using an overlapping domain decomposition approach in combination with execution of multiple threads that solve chemical equilibria in parallel. FE reactive transport schemes are often affected by spurious concentration oscillations. We effectively suppress these oscillations with a linearized algebraic flux corrected transport (FCT) algorithm. An application example is presented which investigates the evolution of material interfaces in a deep geological repository for nuclear waste. The example uses all features of the new coupled code: flow and multi-component transport in variably saturated media, and a very complex chemical setup which makes extensive use of (non-linear) solid solution formulations for mineral phases.     

Simulation of density-driven flow in fractured porous media

We study density-driven flow in a fractured porous medium in which the fractures are represented as manifolds of reduced dimensionality. Fractures are assumed to be thin regions of space filled with a porous material whose properties differ from those of the porous medium enclosing them. The interfaces separating the fractures from the embedding medium are assumed to be ideal. We consider two approaches: (i) the fractures have the same dimension, d, as the embedding medium and are said to be d-dimensional; (ii) the fractures are considered as (d − 1)-dimensional manifolds, and the equations of density-driven flow are found by averaging the d-dimensional laws over the fracture width. We show that the second approach is a valid alternative to the first one. For this purpose, we perform numerical experiments using finite-volume discretization for both approaches. The results obtained by the two methods are in good agreement with each other.     

Modeling plume behavior for nonlinearly sorbing solutes in saturated homogeneous porous media

Transport of a sorbing solute in a two-dimensional steady and uniform flow field is modeled using a particle tracking random walk method. The solute is initially introduced from an instantaneous point source. Cases of linear and nonlinear sorption isotherms are considered. Local pore velocity and mechanical dispersion are used to describe the solute transport mechanisms at the local scale. The numerical simulation of solute particle transport yields the large scale behavior of the solute plume. Behavior of the plume is quantified in terms of the center-of-mass displacement distance, relative velocity of the center-of-mass, mass breakthrough curves, spread variance, and longitudinal skewness. The nonlinear sorption isotherm affects the plume behavior in the following way relative to the linear isotherm: (1) the plume velocity decreases exponentially with time; (2) the longitudinal variance increases nonlinearly with time; (3) the solute front is steepened and tailing is enhanced     

饱和多孔介质近场波动分析的一种黏弹性人工边界

采用有限模型数值方法求解能量开放系统中的波动问题时,虚拟人工边界的处理方式对计算结果的准确性和精度具有重要的影响.本文针对无限域饱和多孔介质中波传播问题的人工边界处理方式进行了研究,提出了饱和多孔介质近场波动分析的一种黏弹性人工边界处理方法.在考虑多孔介质中固相和液相的相互作用的情况下,通过在人工边界处分别施加反映固相和液相介质波传播效应的弹簧及阻尼来模拟饱和多孔介质中波的能量辐射效应影响.算例表明,本文建议的黏弹性人工边界具有较好的模拟效果.     

Analytical approximations for flow in compressible,saturated, one-dimensional porous media

A nonlinear model for single-phase fluid flow in slightly compressible porous media is presented and solved approximately. The model assumes state equations for density, porosity, viscosity and permeability that are exponential functions of the fluid (either gas or liquid) pressure. The governing equation is transformed into a nonlinear diffusion equation. It is solved for a semi-infinite domain for either constant pressure or constant flux boundary conditions at the surface. The solutions obtained, although approximate, are extremely accurate as demonstrated by comparisons with numerical results. Predictions for the surface pressure resulting from a constant flux into a porous medium are compared with published experimental data.     

基于Kelvin-Voigt黏弹性骨架的含非饱和流体孔隙介质BISQ模型(英文)

本文综合考虑了在波传播过程中孔隙介质的三种重要力学机制——"Biot流动机制一squirt流动机制-固体骨架黏弹性机制",借鉴等效介质思想,将含水饱和度引入波动力学控制方程,并考虑了不同波频率下孔隙流体分布模式对其等效体积模量的影响,给出了能处理含粘滞性非饱和流体孔隙介质中波传播问题的黏弹性Biot/squirt(BISQ)模型。推导了时间-空间域的波动力学方程组,由一组平面谐波解假设,给出频率-波数域黏弹性BISQ模型的相速度和衰减系数表达式。基于数值算例分析了含水饱和度、渗透率与频率对纵波速度和衰减的影响,并结合致密砂岩和碳酸盐岩的实测数据,对非饱和情况下的储层纵波速度进行了外推,碳酸盐岩储层中纵波速度对含气饱和度的敏感性明显低于砂岩储层。     

Velocity dispersion and fluid substitution in sandstone under partially saturated conditions

The elastic moduli of four sandstone samples are measured at seismic (2?2000 Hz) and ultrasonic (1 MHz) frequencies and water- and glycerin-saturated conditions. We observe that the high-permeability samples under partially water-saturated conditions and the low-permeability samples under partially glycerin-saturated conditions show little dispersion at low frequencies (2?2000 Hz). However, the high-permeability samples under partially glycerin-saturated conditions and the low-permeability samples under partially water-saturated conditions produce strong dispersion in the same frequency range (2?2000 Hz). This suggests that fluid mobility largely controls the pore-fluid movement and pore pressure in a porous medium. High fluid mobility facilitates pore-pressure equilibration either between pores or between heterogeneous regions, resulting in a low-frequency domain where the Gassmann equations are valid. In contrast, low fluid mobility produces pressure gradients even at seismic frequencies, and thus dispersion. The latter shows a systematic shift to lower frequencies with decreasing mobility. Sandstone samples showed variations in V_p as a function of fluid saturation. We explore the applicability of the Gassmann model on sandstone rocks. Two theoretical bounds for the P-velocity are known, the Gassmann–Wood and Gassmann–Hill limits. The observations confirm the effect of wave-induced flow on the transition from the Gassmann–Wood to the Gassmann–Hill limit. With decreasing fluid mobility, the P-velocity at 2–2000 Hz moves from the Gassmann–Wood boundary to the Gassmann–Hill boundary. In addition,, we investigate the mechanisms responsible for this transition.